Indifferent front

On February 3,1956, Autherine Lucy became the first African-American student to attend the University of Alabama, although the dean of women refused to allow Autherine to live in a university dormitory. White students rioted in protest of her admission, and the federal government had to assume command of the Alabama National Guard in order to protect her. Nonetheless, on her first day in class, Autherine bravely took a seat in the front row. She remembers being surprised that the professor of the class appeared not to notice she was even in class. Later, she would appreciate his seeming indifference, as he was one of only a few professors to speak out in favor of her right to attend the university. 

Figure 2.9. For Isotherm 2, which is hnear, = 0.08 and 5l = 0, or Cj = 0.08Q. The calculation is presented in Table 2.4, and the locations of different solute concentrations after one PV solution injection are shown in Figure 2.11. For the linear adsorption, the concentration is delayed, while the shape of the concentration front remains unchanged. Such a front is called an indifferent front, which occurs when the slope of the adsorption isotherm is independent of concentration (constant), or the velocities of different concentrations are the same.

FIGURE 2.11 Indifferent front when the adsorption is linear. 

To discern whether a front is sharpening, we compare the velocities at the initial concentration and final concentration. If the velocity at the final concentration is higher than that at the initial concentration, the front will be a sharpening front, or shock. In the opposite situation, in which the velocity at the final concentration is lower than that at the initial concentration, the front will be a spreading front or broadening front. If the velocity is independent of the concentration, the front will be an indifferent front. To discern the types of fronts, some (e.g.. Pope, 1980) compare the upstream and downstream velocities that correspond to the velocities at the final and initial concentrations, the terms used here. 

Different crystallographic planes of a semiconductor electrode usually exhibit different reaction kinetics. It was found in III-V compounds in indifferent electrolytes that the (lll)B face terminated with the anion plane (P, As) etched faster than the (lll)A face containing the cations (Ga, In) [47]. The planes composed entirely of metal atoms react more slowly than any other crystal plane because of the stable metal oxide layer, which can be formed on such planes. Consequently on these planes termed etch stop planes, provision of reactants (diffusion control) is not rate-limiting. In Si, the (100) planes are known to etch faster than (111) planes in alkaline solutions. This property is at the origin of various apphcations, such as texturization of silicon surface [formation of pyramids on (100) planes], which allows reduction of reflectivity of the front surface of solar cells and Si micromachining [48]. The semiconductor surface may be shaped during the anodic dissolution... 

If the function f(f) is derivable, the term between brackets vanishes and the relationship in Equation 9.120 is demonstrated. It can be remarked that the coefficient in front of the integral operator in the Fourier definition is indifferent in this demonstration it plays only the role of a normalizing factor for having a unitary transform, that is, which gives the same resnlt when using the inverse transform (which is written in a symmetrical expression by changing jnst the sign of the parameter co). 

Discretize the objective space into hyperboxes with user-defined indifference thresholds, and then represent the Pareto-optimal front with a collection of hyperboxes. 

---